Final answer:
To determine if the triangle is a right triangle, the Pythagorean theorem is applied. Upon calculation, the triangle with sides 33 km, 56 km, and 65 km satisfies the theorem, confirming it is a right triangle.
Step-by-step explanation:
To determine whether a triangle with sides of 33 kilometers, 56 kilometers, and 65 kilometers is a right triangle, we can apply the Pythagorean theorem. The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), mathematically expressed as a² + b² = c².
To verify if our triangle is a right triangle, we can substitute the side lengths into the Pythagorean theorem equation:
33² + 56² = 65²
1089 + 3136 = 4225
4225 = 4225
Since the sum of the squares of the two shorter sides equals the square of the longest side, the triangle with sides of 33 km, 56 km, and 65 km is indeed a right triangle.